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A252964
Number of (3+2) X (n+2) 0..4 arrays with every consecutive three elements in every row and diagonal having exactly two distinct values, and in every column and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order.
1
297, 185, 259, 369, 605, 985, 1429, 2421, 3907, 6027, 9989, 16623, 25801, 43767, 71599, 116257, 192617, 324273, 522253, 887501, 1465051, 2445931, 4064909, 6900751, 11349313, 19365335, 32221303, 54651057, 91301921, 156087937
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = a(n-1) + 6*a(n-2) - a(n-3) - 15*a(n-4) - 20*a(n-5) + 27*a(n-6) + 53*a(n-7) - 14*a(n-8) - 51*a(n-9) - 45*a(n-10) + 60*a(n-11) + 18*a(n-12) - 18*a(n-13) for n>15.
Empirical g.f.: x*(297 - 112*x - 1708*x^2 - 703*x^3 + 3322*x^4 + 7140*x^5 - 3251*x^6 - 14334*x^7 - 2288*x^8 + 9945*x^9 + 14610*x^10 - 10506*x^11 - 5994*x^12 + 3384*x^13 + 216*x^14) / ((1 - x)*(1 + x - x^2)*(1 - x - x^2)*(1 - 3*x^2)*(1 - 2*x^3)*(1 - 3*x^3)). - Colin Barker, Dec 07 2018
EXAMPLE
Some solutions for n=2:
..0..1..0..0....0..1..1..2....0..1..1..2....0..1..1..2....0..0..1..1
..1..2..1..1....1..0..1..1....2..2..3..3....2..0..0..1....2..2..3..3
..3..3..2..2....3..3..1..3....3..0..0..1....3..4..4..0....4..4..0..0
..4..4..3..4....2..1..1..0....4..4..2..2....1..2..2..4....1..1..2..2
..1..1..4..1....1..2..1..1....1..3..3..0....0..3..3..2....3..3..4..4
CROSSREFS
Row 3 of A252961.
Sequence in context: A223847 A223873 A223798 * A224601 A372249 A134260
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 25 2014
STATUS
approved